Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0879326623\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.81326 | −1.62424 | −0.812119 | − | 0.583491i | \(-0.801686\pi\) | ||||
−0.812119 | + | 0.583491i | \(0.801686\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.734328 | −0.328401 | −0.164201 | − | 0.986427i | \(-0.552504\pi\) | ||||
−0.164201 | + | 0.986427i | \(0.552504\pi\) | |||||||
\(6\) | −2.81326 | −1.14851 | ||||||||
\(7\) | −3.92682 | −1.48420 | −0.742100 | − | 0.670289i | \(-0.766170\pi\) | ||||
−0.742100 | + | 0.670289i | \(0.766170\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.91446 | 1.63815 | ||||||||
\(10\) | −0.734328 | −0.232215 | ||||||||
\(11\) | −2.05575 | −0.619833 | −0.309916 | − | 0.950764i | \(-0.600301\pi\) | ||||
−0.309916 | + | 0.950764i | \(0.600301\pi\) | |||||||
\(12\) | −2.81326 | −0.812119 | ||||||||
\(13\) | 2.59713 | 0.720316 | 0.360158 | − | 0.932891i | \(-0.382723\pi\) | ||||
0.360158 | + | 0.932891i | \(0.382723\pi\) | |||||||
\(14\) | −3.92682 | −1.04949 | ||||||||
\(15\) | 2.06586 | 0.533402 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.17872 | −0.528418 | −0.264209 | − | 0.964465i | \(-0.585111\pi\) | ||||
−0.264209 | + | 0.964465i | \(0.585111\pi\) | |||||||
\(18\) | 4.91446 | 1.15835 | ||||||||
\(19\) | 2.47344 | 0.567447 | 0.283723 | − | 0.958906i | \(-0.408430\pi\) | ||||
0.283723 | + | 0.958906i | \(0.408430\pi\) | |||||||
\(20\) | −0.734328 | −0.164201 | ||||||||
\(21\) | 11.0472 | 2.41069 | ||||||||
\(22\) | −2.05575 | −0.438288 | ||||||||
\(23\) | −7.75830 | −1.61772 | −0.808859 | − | 0.588003i | \(-0.799914\pi\) | ||||
−0.808859 | + | 0.588003i | \(0.799914\pi\) | |||||||
\(24\) | −2.81326 | −0.574255 | ||||||||
\(25\) | −4.46076 | −0.892153 | ||||||||
\(26\) | 2.59713 | 0.509340 | ||||||||
\(27\) | −5.38587 | −1.03651 | ||||||||
\(28\) | −3.92682 | −0.742100 | ||||||||
\(29\) | −0.714090 | −0.132603 | −0.0663016 | − | 0.997800i | \(-0.521120\pi\) | ||||
−0.0663016 | + | 0.997800i | \(0.521120\pi\) | |||||||
\(30\) | 2.06586 | 0.377172 | ||||||||
\(31\) | −6.19809 | −1.11321 | −0.556605 | − | 0.830777i | \(-0.687896\pi\) | ||||
−0.556605 | + | 0.830777i | \(0.687896\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.78338 | 1.00676 | ||||||||
\(34\) | −2.17872 | −0.373648 | ||||||||
\(35\) | 2.88358 | 0.487413 | ||||||||
\(36\) | 4.91446 | 0.819076 | ||||||||
\(37\) | 1.58273 | 0.260199 | 0.130100 | − | 0.991501i | \(-0.458470\pi\) | ||||
0.130100 | + | 0.991501i | \(0.458470\pi\) | |||||||
\(38\) | 2.47344 | 0.401246 | ||||||||
\(39\) | −7.30643 | −1.16996 | ||||||||
\(40\) | −0.734328 | −0.116107 | ||||||||
\(41\) | 1.17904 | 0.184135 | 0.0920676 | − | 0.995753i | \(-0.470652\pi\) | ||||
0.0920676 | + | 0.995753i | \(0.470652\pi\) | |||||||
\(42\) | 11.0472 | 1.70462 | ||||||||
\(43\) | −2.12532 | −0.324109 | −0.162054 | − | 0.986782i | \(-0.551812\pi\) | ||||
−0.162054 | + | 0.986782i | \(0.551812\pi\) | |||||||
\(44\) | −2.05575 | −0.309916 | ||||||||
\(45\) | −3.60882 | −0.537971 | ||||||||
\(46\) | −7.75830 | −1.14390 | ||||||||
\(47\) | −6.14523 | −0.896374 | −0.448187 | − | 0.893940i | \(-0.647930\pi\) | ||||
−0.448187 | + | 0.893940i | \(0.647930\pi\) | |||||||
\(48\) | −2.81326 | −0.406060 | ||||||||
\(49\) | 8.41994 | 1.20285 | ||||||||
\(50\) | −4.46076 | −0.630847 | ||||||||
\(51\) | 6.12932 | 0.858277 | ||||||||
\(52\) | 2.59713 | 0.360158 | ||||||||
\(53\) | 7.69092 | 1.05643 | 0.528215 | − | 0.849111i | \(-0.322862\pi\) | ||||
0.528215 | + | 0.849111i | \(0.322862\pi\) | |||||||
\(54\) | −5.38587 | −0.732924 | ||||||||
\(55\) | 1.50960 | 0.203554 | ||||||||
\(56\) | −3.92682 | −0.524744 | ||||||||
\(57\) | −6.95845 | −0.921669 | ||||||||
\(58\) | −0.714090 | −0.0937646 | ||||||||
\(59\) | −5.97592 | −0.777998 | −0.388999 | − | 0.921238i | \(-0.627179\pi\) | ||||
−0.388999 | + | 0.921238i | \(0.627179\pi\) | |||||||
\(60\) | 2.06586 | 0.266701 | ||||||||
\(61\) | 8.67190 | 1.11032 | 0.555161 | − | 0.831743i | \(-0.312656\pi\) | ||||
0.555161 | + | 0.831743i | \(0.312656\pi\) | |||||||
\(62\) | −6.19809 | −0.787159 | ||||||||
\(63\) | −19.2982 | −2.43134 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.90715 | −0.236553 | ||||||||
\(66\) | 5.78338 | 0.711885 | ||||||||
\(67\) | −0.00760682 | −0.000929321 0 | −0.000464660 | − | 1.00000i | \(-0.500148\pi\) | ||||
−0.000464660 | 1.00000i | \(0.500148\pi\) | ||||||||
\(68\) | −2.17872 | −0.264209 | ||||||||
\(69\) | 21.8261 | 2.62756 | ||||||||
\(70\) | 2.88358 | 0.344653 | ||||||||
\(71\) | −12.4138 | −1.47324 | −0.736622 | − | 0.676304i | \(-0.763580\pi\) | ||||
−0.736622 | + | 0.676304i | \(0.763580\pi\) | |||||||
\(72\) | 4.91446 | 0.579174 | ||||||||
\(73\) | −10.4390 | −1.22180 | −0.610898 | − | 0.791709i | \(-0.709191\pi\) | ||||
−0.610898 | + | 0.791709i | \(0.709191\pi\) | |||||||
\(74\) | 1.58273 | 0.183989 | ||||||||
\(75\) | 12.5493 | 1.44907 | ||||||||
\(76\) | 2.47344 | 0.283723 | ||||||||
\(77\) | 8.07258 | 0.919956 | ||||||||
\(78\) | −7.30643 | −0.827290 | ||||||||
\(79\) | 3.87181 | 0.435612 | 0.217806 | − | 0.975992i | \(-0.430110\pi\) | ||||
0.217806 | + | 0.975992i | \(0.430110\pi\) | |||||||
\(80\) | −0.734328 | −0.0821003 | ||||||||
\(81\) | 0.408511 | 0.0453902 | ||||||||
\(82\) | 1.17904 | 0.130203 | ||||||||
\(83\) | −10.7691 | −1.18206 | −0.591029 | − | 0.806651i | \(-0.701278\pi\) | ||||
−0.591029 | + | 0.806651i | \(0.701278\pi\) | |||||||
\(84\) | 11.0472 | 1.20535 | ||||||||
\(85\) | 1.59990 | 0.173533 | ||||||||
\(86\) | −2.12532 | −0.229180 | ||||||||
\(87\) | 2.00892 | 0.215379 | ||||||||
\(88\) | −2.05575 | −0.219144 | ||||||||
\(89\) | −3.74793 | −0.397280 | −0.198640 | − | 0.980073i | \(-0.563652\pi\) | ||||
−0.198640 | + | 0.980073i | \(0.563652\pi\) | |||||||
\(90\) | −3.60882 | −0.380403 | ||||||||
\(91\) | −10.1985 | −1.06909 | ||||||||
\(92\) | −7.75830 | −0.808859 | ||||||||
\(93\) | 17.4369 | 1.80812 | ||||||||
\(94\) | −6.14523 | −0.633832 | ||||||||
\(95\) | −1.81632 | −0.186350 | ||||||||
\(96\) | −2.81326 | −0.287128 | ||||||||
\(97\) | −10.1396 | −1.02952 | −0.514759 | − | 0.857335i | \(-0.672119\pi\) | ||||
−0.514759 | + | 0.857335i | \(0.672119\pi\) | |||||||
\(98\) | 8.41994 | 0.850542 | ||||||||
\(99\) | −10.1029 | −1.01538 | ||||||||
\(100\) | −4.46076 | −0.446076 | ||||||||
\(101\) | 9.52351 | 0.947624 | 0.473812 | − | 0.880626i | \(-0.342878\pi\) | ||||
0.473812 | + | 0.880626i | \(0.342878\pi\) | |||||||
\(102\) | 6.12932 | 0.606893 | ||||||||
\(103\) | −5.88240 | −0.579610 | −0.289805 | − | 0.957086i | \(-0.593590\pi\) | ||||
−0.289805 | + | 0.957086i | \(0.593590\pi\) | |||||||
\(104\) | 2.59713 | 0.254670 | ||||||||
\(105\) | −8.11226 | −0.791675 | ||||||||
\(106\) | 7.69092 | 0.747008 | ||||||||
\(107\) | 3.55489 | 0.343664 | 0.171832 | − | 0.985126i | \(-0.445031\pi\) | ||||
0.171832 | + | 0.985126i | \(0.445031\pi\) | |||||||
\(108\) | −5.38587 | −0.518256 | ||||||||
\(109\) | −11.2797 | −1.08040 | −0.540198 | − | 0.841538i | \(-0.681651\pi\) | ||||
−0.540198 | + | 0.841538i | \(0.681651\pi\) | |||||||
\(110\) | 1.50960 | 0.143934 | ||||||||
\(111\) | −4.45264 | −0.422626 | ||||||||
\(112\) | −3.92682 | −0.371050 | ||||||||
\(113\) | 5.24049 | 0.492984 | 0.246492 | − | 0.969145i | \(-0.420722\pi\) | ||||
0.246492 | + | 0.969145i | \(0.420722\pi\) | |||||||
\(114\) | −6.95845 | −0.651719 | ||||||||
\(115\) | 5.69713 | 0.531260 | ||||||||
\(116\) | −0.714090 | −0.0663016 | ||||||||
\(117\) | 12.7635 | 1.17999 | ||||||||
\(118\) | −5.97592 | −0.550128 | ||||||||
\(119\) | 8.55546 | 0.784278 | ||||||||
\(120\) | 2.06586 | 0.188586 | ||||||||
\(121\) | −6.77388 | −0.615807 | ||||||||
\(122\) | 8.67190 | 0.785117 | ||||||||
\(123\) | −3.31695 | −0.299080 | ||||||||
\(124\) | −6.19809 | −0.556605 | ||||||||
\(125\) | 6.94730 | 0.621385 | ||||||||
\(126\) | −19.2982 | −1.71922 | ||||||||
\(127\) | −11.8477 | −1.05131 | −0.525656 | − | 0.850697i | \(-0.676180\pi\) | ||||
−0.525656 | + | 0.850697i | \(0.676180\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.97910 | 0.526430 | ||||||||
\(130\) | −1.90715 | −0.167268 | ||||||||
\(131\) | 21.8323 | 1.90750 | 0.953750 | − | 0.300600i | \(-0.0971869\pi\) | ||||
0.953750 | + | 0.300600i | \(0.0971869\pi\) | |||||||
\(132\) | 5.78338 | 0.503378 | ||||||||
\(133\) | −9.71277 | −0.842204 | ||||||||
\(134\) | −0.00760682 | −0.000657129 0 | ||||||||
\(135\) | 3.95499 | 0.340392 | ||||||||
\(136\) | −2.17872 | −0.186824 | ||||||||
\(137\) | −3.92644 | −0.335458 | −0.167729 | − | 0.985833i | \(-0.553643\pi\) | ||||
−0.167729 | + | 0.985833i | \(0.553643\pi\) | |||||||
\(138\) | 21.8261 | 1.85796 | ||||||||
\(139\) | −1.42264 | −0.120667 | −0.0603335 | − | 0.998178i | \(-0.519216\pi\) | ||||
−0.0603335 | + | 0.998178i | \(0.519216\pi\) | |||||||
\(140\) | 2.88358 | 0.243707 | ||||||||
\(141\) | 17.2882 | 1.45593 | ||||||||
\(142\) | −12.4138 | −1.04174 | ||||||||
\(143\) | −5.33907 | −0.446475 | ||||||||
\(144\) | 4.91446 | 0.409538 | ||||||||
\(145\) | 0.524376 | 0.0435471 | ||||||||
\(146\) | −10.4390 | −0.863940 | ||||||||
\(147\) | −23.6875 | −1.95371 | ||||||||
\(148\) | 1.58273 | 0.130100 | ||||||||
\(149\) | 17.9742 | 1.47250 | 0.736250 | − | 0.676709i | \(-0.236595\pi\) | ||||
0.736250 | + | 0.676709i | \(0.236595\pi\) | |||||||
\(150\) | 12.5493 | 1.02465 | ||||||||
\(151\) | −8.24330 | −0.670830 | −0.335415 | − | 0.942070i | \(-0.608877\pi\) | ||||
−0.335415 | + | 0.942070i | \(0.608877\pi\) | |||||||
\(152\) | 2.47344 | 0.200623 | ||||||||
\(153\) | −10.7072 | −0.865629 | ||||||||
\(154\) | 8.07258 | 0.650507 | ||||||||
\(155\) | 4.55143 | 0.365580 | ||||||||
\(156\) | −7.30643 | −0.584982 | ||||||||
\(157\) | −3.92699 | −0.313408 | −0.156704 | − | 0.987646i | \(-0.550087\pi\) | ||||
−0.156704 | + | 0.987646i | \(0.550087\pi\) | |||||||
\(158\) | 3.87181 | 0.308024 | ||||||||
\(159\) | −21.6366 | −1.71589 | ||||||||
\(160\) | −0.734328 | −0.0580537 | ||||||||
\(161\) | 30.4655 | 2.40102 | ||||||||
\(162\) | 0.408511 | 0.0320957 | ||||||||
\(163\) | 17.3602 | 1.35976 | 0.679878 | − | 0.733325i | \(-0.262033\pi\) | ||||
0.679878 | + | 0.733325i | \(0.262033\pi\) | |||||||
\(164\) | 1.17904 | 0.0920676 | ||||||||
\(165\) | −4.24689 | −0.330620 | ||||||||
\(166\) | −10.7691 | −0.835841 | ||||||||
\(167\) | −3.44601 | −0.266660 | −0.133330 | − | 0.991072i | \(-0.542567\pi\) | ||||
−0.133330 | + | 0.991072i | \(0.542567\pi\) | |||||||
\(168\) | 11.0472 | 0.852309 | ||||||||
\(169\) | −6.25489 | −0.481145 | ||||||||
\(170\) | 1.59990 | 0.122706 | ||||||||
\(171\) | 12.1556 | 0.929564 | ||||||||
\(172\) | −2.12532 | −0.162054 | ||||||||
\(173\) | −16.1607 | −1.22868 | −0.614339 | − | 0.789042i | \(-0.710577\pi\) | ||||
−0.614339 | + | 0.789042i | \(0.710577\pi\) | |||||||
\(174\) | 2.00892 | 0.152296 | ||||||||
\(175\) | 17.5166 | 1.32413 | ||||||||
\(176\) | −2.05575 | −0.154958 | ||||||||
\(177\) | 16.8118 | 1.26365 | ||||||||
\(178\) | −3.74793 | −0.280919 | ||||||||
\(179\) | 19.6283 | 1.46709 | 0.733545 | − | 0.679641i | \(-0.237864\pi\) | ||||
0.733545 | + | 0.679641i | \(0.237864\pi\) | |||||||
\(180\) | −3.60882 | −0.268986 | ||||||||
\(181\) | −10.3399 | −0.768559 | −0.384280 | − | 0.923217i | \(-0.625550\pi\) | ||||
−0.384280 | + | 0.923217i | \(0.625550\pi\) | |||||||
\(182\) | −10.1985 | −0.755962 | ||||||||
\(183\) | −24.3963 | −1.80343 | ||||||||
\(184\) | −7.75830 | −0.571949 | ||||||||
\(185\) | −1.16224 | −0.0854498 | ||||||||
\(186\) | 17.4369 | 1.27853 | ||||||||
\(187\) | 4.47892 | 0.327531 | ||||||||
\(188\) | −6.14523 | −0.448187 | ||||||||
\(189\) | 21.1494 | 1.53839 | ||||||||
\(190\) | −1.81632 | −0.131770 | ||||||||
\(191\) | 17.5770 | 1.27183 | 0.635915 | − | 0.771759i | \(-0.280623\pi\) | ||||
0.635915 | + | 0.771759i | \(0.280623\pi\) | |||||||
\(192\) | −2.81326 | −0.203030 | ||||||||
\(193\) | 5.25574 | 0.378316 | 0.189158 | − | 0.981947i | \(-0.439424\pi\) | ||||
0.189158 | + | 0.981947i | \(0.439424\pi\) | |||||||
\(194\) | −10.1396 | −0.727979 | ||||||||
\(195\) | 5.36531 | 0.384218 | ||||||||
\(196\) | 8.41994 | 0.601424 | ||||||||
\(197\) | −8.47589 | −0.603882 | −0.301941 | − | 0.953327i | \(-0.597635\pi\) | ||||
−0.301941 | + | 0.953327i | \(0.597635\pi\) | |||||||
\(198\) | −10.1029 | −0.717983 | ||||||||
\(199\) | 18.1179 | 1.28434 | 0.642171 | − | 0.766562i | \(-0.278034\pi\) | ||||
0.642171 | + | 0.766562i | \(0.278034\pi\) | |||||||
\(200\) | −4.46076 | −0.315424 | ||||||||
\(201\) | 0.0214000 | 0.00150944 | ||||||||
\(202\) | 9.52351 | 0.670072 | ||||||||
\(203\) | 2.80411 | 0.196810 | ||||||||
\(204\) | 6.12932 | 0.429138 | ||||||||
\(205\) | −0.865803 | −0.0604703 | ||||||||
\(206\) | −5.88240 | −0.409846 | ||||||||
\(207\) | −38.1278 | −2.65007 | ||||||||
\(208\) | 2.59713 | 0.180079 | ||||||||
\(209\) | −5.08479 | −0.351722 | ||||||||
\(210\) | −8.11226 | −0.559799 | ||||||||
\(211\) | −2.84303 | −0.195722 | −0.0978610 | − | 0.995200i | \(-0.531200\pi\) | ||||
−0.0978610 | + | 0.995200i | \(0.531200\pi\) | |||||||
\(212\) | 7.69092 | 0.528215 | ||||||||
\(213\) | 34.9232 | 2.39290 | ||||||||
\(214\) | 3.55489 | 0.243007 | ||||||||
\(215\) | 1.56068 | 0.106438 | ||||||||
\(216\) | −5.38587 | −0.366462 | ||||||||
\(217\) | 24.3388 | 1.65223 | ||||||||
\(218\) | −11.2797 | −0.763956 | ||||||||
\(219\) | 29.3677 | 1.98449 | ||||||||
\(220\) | 1.50960 | 0.101777 | ||||||||
\(221\) | −5.65844 | −0.380628 | ||||||||
\(222\) | −4.45264 | −0.298842 | ||||||||
\(223\) | −19.1545 | −1.28268 | −0.641339 | − | 0.767257i | \(-0.721621\pi\) | ||||
−0.641339 | + | 0.767257i | \(0.721621\pi\) | |||||||
\(224\) | −3.92682 | −0.262372 | ||||||||
\(225\) | −21.9222 | −1.46148 | ||||||||
\(226\) | 5.24049 | 0.348592 | ||||||||
\(227\) | 0.877514 | 0.0582427 | 0.0291213 | − | 0.999576i | \(-0.490729\pi\) | ||||
0.0291213 | + | 0.999576i | \(0.490729\pi\) | |||||||
\(228\) | −6.95845 | −0.460835 | ||||||||
\(229\) | 27.2775 | 1.80255 | 0.901273 | − | 0.433252i | \(-0.142634\pi\) | ||||
0.901273 | + | 0.433252i | \(0.142634\pi\) | |||||||
\(230\) | 5.69713 | 0.375658 | ||||||||
\(231\) | −22.7103 | −1.49423 | ||||||||
\(232\) | −0.714090 | −0.0468823 | ||||||||
\(233\) | 4.79290 | 0.313993 | 0.156997 | − | 0.987599i | \(-0.449819\pi\) | ||||
0.156997 | + | 0.987599i | \(0.449819\pi\) | |||||||
\(234\) | 12.7635 | 0.834376 | ||||||||
\(235\) | 4.51261 | 0.294370 | ||||||||
\(236\) | −5.97592 | −0.388999 | ||||||||
\(237\) | −10.8924 | −0.707538 | ||||||||
\(238\) | 8.55546 | 0.554568 | ||||||||
\(239\) | 14.2751 | 0.923378 | 0.461689 | − | 0.887042i | \(-0.347244\pi\) | ||||
0.461689 | + | 0.887042i | \(0.347244\pi\) | |||||||
\(240\) | 2.06586 | 0.133351 | ||||||||
\(241\) | 1.24232 | 0.0800248 | 0.0400124 | − | 0.999199i | \(-0.487260\pi\) | ||||
0.0400124 | + | 0.999199i | \(0.487260\pi\) | |||||||
\(242\) | −6.77388 | −0.435441 | ||||||||
\(243\) | 15.0084 | 0.962787 | ||||||||
\(244\) | 8.67190 | 0.555161 | ||||||||
\(245\) | −6.18300 | −0.395017 | ||||||||
\(246\) | −3.31695 | −0.211481 | ||||||||
\(247\) | 6.42387 | 0.408741 | ||||||||
\(248\) | −6.19809 | −0.393579 | ||||||||
\(249\) | 30.2962 | 1.91994 | ||||||||
\(250\) | 6.94730 | 0.439386 | ||||||||
\(251\) | −21.9668 | −1.38653 | −0.693266 | − | 0.720682i | \(-0.743829\pi\) | ||||
−0.693266 | + | 0.720682i | \(0.743829\pi\) | |||||||
\(252\) | −19.2982 | −1.21567 | ||||||||
\(253\) | 15.9491 | 1.00271 | ||||||||
\(254\) | −11.8477 | −0.743390 | ||||||||
\(255\) | −4.50093 | −0.281859 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.00777 | 0.374754 | 0.187377 | − | 0.982288i | \(-0.440001\pi\) | ||||
0.187377 | + | 0.982288i | \(0.440001\pi\) | |||||||
\(258\) | 5.97910 | 0.372242 | ||||||||
\(259\) | −6.21511 | −0.386188 | ||||||||
\(260\) | −1.90715 | −0.118276 | ||||||||
\(261\) | −3.50937 | −0.217224 | ||||||||
\(262\) | 21.8323 | 1.34881 | ||||||||
\(263\) | 26.7329 | 1.64842 | 0.824212 | − | 0.566281i | \(-0.191618\pi\) | ||||
0.824212 | + | 0.566281i | \(0.191618\pi\) | |||||||
\(264\) | 5.78338 | 0.355942 | ||||||||
\(265\) | −5.64766 | −0.346933 | ||||||||
\(266\) | −9.71277 | −0.595528 | ||||||||
\(267\) | 10.5439 | 0.645278 | ||||||||
\(268\) | −0.00760682 | −0.000464660 0 | ||||||||
\(269\) | −18.4790 | −1.12669 | −0.563343 | − | 0.826223i | \(-0.690485\pi\) | ||||
−0.563343 | + | 0.826223i | \(0.690485\pi\) | |||||||
\(270\) | 3.95499 | 0.240693 | ||||||||
\(271\) | 27.7761 | 1.68728 | 0.843638 | − | 0.536912i | \(-0.180409\pi\) | ||||
0.843638 | + | 0.536912i | \(0.180409\pi\) | |||||||
\(272\) | −2.17872 | −0.132104 | ||||||||
\(273\) | 28.6910 | 1.73646 | ||||||||
\(274\) | −3.92644 | −0.237205 | ||||||||
\(275\) | 9.17023 | 0.552986 | ||||||||
\(276\) | 21.8261 | 1.31378 | ||||||||
\(277\) | −8.76025 | −0.526353 | −0.263176 | − | 0.964748i | \(-0.584770\pi\) | ||||
−0.263176 | + | 0.964748i | \(0.584770\pi\) | |||||||
\(278\) | −1.42264 | −0.0853245 | ||||||||
\(279\) | −30.4603 | −1.82361 | ||||||||
\(280\) | 2.88358 | 0.172327 | ||||||||
\(281\) | 24.5807 | 1.46636 | 0.733181 | − | 0.680034i | \(-0.238035\pi\) | ||||
0.733181 | + | 0.680034i | \(0.238035\pi\) | |||||||
\(282\) | 17.2882 | 1.02949 | ||||||||
\(283\) | 11.9549 | 0.710645 | 0.355322 | − | 0.934744i | \(-0.384371\pi\) | ||||
0.355322 | + | 0.934744i | \(0.384371\pi\) | |||||||
\(284\) | −12.4138 | −0.736622 | ||||||||
\(285\) | 5.10978 | 0.302677 | ||||||||
\(286\) | −5.33907 | −0.315706 | ||||||||
\(287\) | −4.62989 | −0.273294 | ||||||||
\(288\) | 4.91446 | 0.289587 | ||||||||
\(289\) | −12.2532 | −0.720775 | ||||||||
\(290\) | 0.524376 | 0.0307924 | ||||||||
\(291\) | 28.5253 | 1.67218 | ||||||||
\(292\) | −10.4390 | −0.610898 | ||||||||
\(293\) | 16.6317 | 0.971636 | 0.485818 | − | 0.874060i | \(-0.338522\pi\) | ||||
0.485818 | + | 0.874060i | \(0.338522\pi\) | |||||||
\(294\) | −23.6875 | −1.38148 | ||||||||
\(295\) | 4.38828 | 0.255496 | ||||||||
\(296\) | 1.58273 | 0.0919944 | ||||||||
\(297\) | 11.0720 | 0.642464 | ||||||||
\(298\) | 17.9742 | 1.04122 | ||||||||
\(299\) | −20.1493 | −1.16527 | ||||||||
\(300\) | 12.5493 | 0.724534 | ||||||||
\(301\) | 8.34577 | 0.481042 | ||||||||
\(302\) | −8.24330 | −0.474349 | ||||||||
\(303\) | −26.7921 | −1.53917 | ||||||||
\(304\) | 2.47344 | 0.141862 | ||||||||
\(305\) | −6.36802 | −0.364632 | ||||||||
\(306\) | −10.7072 | −0.612092 | ||||||||
\(307\) | 26.9050 | 1.53555 | 0.767774 | − | 0.640721i | \(-0.221364\pi\) | ||||
0.767774 | + | 0.640721i | \(0.221364\pi\) | |||||||
\(308\) | 8.07258 | 0.459978 | ||||||||
\(309\) | 16.5487 | 0.941425 | ||||||||
\(310\) | 4.55143 | 0.258504 | ||||||||
\(311\) | 22.3242 | 1.26589 | 0.632943 | − | 0.774198i | \(-0.281847\pi\) | ||||
0.632943 | + | 0.774198i | \(0.281847\pi\) | |||||||
\(312\) | −7.30643 | −0.413645 | ||||||||
\(313\) | 22.4422 | 1.26851 | 0.634254 | − | 0.773124i | \(-0.281307\pi\) | ||||
0.634254 | + | 0.773124i | \(0.281307\pi\) | |||||||
\(314\) | −3.92699 | −0.221613 | ||||||||
\(315\) | 14.1712 | 0.798457 | ||||||||
\(316\) | 3.87181 | 0.217806 | ||||||||
\(317\) | 3.53246 | 0.198403 | 0.0992015 | − | 0.995067i | \(-0.468371\pi\) | ||||
0.0992015 | + | 0.995067i | \(0.468371\pi\) | |||||||
\(318\) | −21.6366 | −1.21332 | ||||||||
\(319\) | 1.46799 | 0.0821919 | ||||||||
\(320\) | −0.734328 | −0.0410502 | ||||||||
\(321\) | −10.0008 | −0.558192 | ||||||||
\(322\) | 30.4655 | 1.69777 | ||||||||
\(323\) | −5.38895 | −0.299849 | ||||||||
\(324\) | 0.408511 | 0.0226951 | ||||||||
\(325\) | −11.5852 | −0.642631 | ||||||||
\(326\) | 17.3602 | 0.961493 | ||||||||
\(327\) | 31.7327 | 1.75482 | ||||||||
\(328\) | 1.17904 | 0.0651017 | ||||||||
\(329\) | 24.1312 | 1.33040 | ||||||||
\(330\) | −4.24689 | −0.233784 | ||||||||
\(331\) | 2.89771 | 0.159273 | 0.0796364 | − | 0.996824i | \(-0.474624\pi\) | ||||
0.0796364 | + | 0.996824i | \(0.474624\pi\) | |||||||
\(332\) | −10.7691 | −0.591029 | ||||||||
\(333\) | 7.77826 | 0.426246 | ||||||||
\(334\) | −3.44601 | −0.188557 | ||||||||
\(335\) | 0.00558590 | 0.000305190 0 | ||||||||
\(336\) | 11.0472 | 0.602674 | ||||||||
\(337\) | 20.0941 | 1.09460 | 0.547299 | − | 0.836937i | \(-0.315656\pi\) | ||||
0.547299 | + | 0.836937i | \(0.315656\pi\) | |||||||
\(338\) | −6.25489 | −0.340221 | ||||||||
\(339\) | −14.7429 | −0.800723 | ||||||||
\(340\) | 1.59990 | 0.0867666 | ||||||||
\(341\) | 12.7418 | 0.690005 | ||||||||
\(342\) | 12.1556 | 0.657301 | ||||||||
\(343\) | −5.57585 | −0.301068 | ||||||||
\(344\) | −2.12532 | −0.114590 | ||||||||
\(345\) | −16.0275 | −0.862894 | ||||||||
\(346\) | −16.1607 | −0.868807 | ||||||||
\(347\) | −4.72179 | −0.253479 | −0.126740 | − | 0.991936i | \(-0.540451\pi\) | ||||
−0.126740 | + | 0.991936i | \(0.540451\pi\) | |||||||
\(348\) | 2.00892 | 0.107690 | ||||||||
\(349\) | 30.4172 | 1.62820 | 0.814099 | − | 0.580726i | \(-0.197231\pi\) | ||||
0.814099 | + | 0.580726i | \(0.197231\pi\) | |||||||
\(350\) | 17.5166 | 0.936303 | ||||||||
\(351\) | −13.9878 | −0.746615 | ||||||||
\(352\) | −2.05575 | −0.109572 | ||||||||
\(353\) | 18.0228 | 0.959258 | 0.479629 | − | 0.877471i | \(-0.340771\pi\) | ||||
0.479629 | + | 0.877471i | \(0.340771\pi\) | |||||||
\(354\) | 16.8118 | 0.893539 | ||||||||
\(355\) | 9.11578 | 0.483816 | ||||||||
\(356\) | −3.74793 | −0.198640 | ||||||||
\(357\) | −24.0688 | −1.27385 | ||||||||
\(358\) | 19.6283 | 1.03739 | ||||||||
\(359\) | −9.99489 | −0.527510 | −0.263755 | − | 0.964590i | \(-0.584961\pi\) | ||||
−0.263755 | + | 0.964590i | \(0.584961\pi\) | |||||||
\(360\) | −3.60882 | −0.190202 | ||||||||
\(361\) | −12.8821 | −0.678004 | ||||||||
\(362\) | −10.3399 | −0.543454 | ||||||||
\(363\) | 19.0567 | 1.00022 | ||||||||
\(364\) | −10.1985 | −0.534546 | ||||||||
\(365\) | 7.66567 | 0.401239 | ||||||||
\(366\) | −24.3963 | −1.27522 | ||||||||
\(367\) | 4.60952 | 0.240615 | 0.120307 | − | 0.992737i | \(-0.461612\pi\) | ||||
0.120307 | + | 0.992737i | \(0.461612\pi\) | |||||||
\(368\) | −7.75830 | −0.404429 | ||||||||
\(369\) | 5.79435 | 0.301642 | ||||||||
\(370\) | −1.16224 | −0.0604222 | ||||||||
\(371\) | −30.2009 | −1.56795 | ||||||||
\(372\) | 17.4369 | 0.904060 | ||||||||
\(373\) | −28.6127 | −1.48151 | −0.740754 | − | 0.671776i | \(-0.765532\pi\) | ||||
−0.740754 | + | 0.671776i | \(0.765532\pi\) | |||||||
\(374\) | 4.47892 | 0.231599 | ||||||||
\(375\) | −19.5446 | −1.00928 | ||||||||
\(376\) | −6.14523 | −0.316916 | ||||||||
\(377\) | −1.85459 | −0.0955162 | ||||||||
\(378\) | 21.1494 | 1.08781 | ||||||||
\(379\) | −21.0909 | −1.08337 | −0.541684 | − | 0.840582i | \(-0.682213\pi\) | ||||
−0.541684 | + | 0.840582i | \(0.682213\pi\) | |||||||
\(380\) | −1.81632 | −0.0931752 | ||||||||
\(381\) | 33.3307 | 1.70758 | ||||||||
\(382\) | 17.5770 | 0.899320 | ||||||||
\(383\) | 37.0129 | 1.89127 | 0.945635 | − | 0.325229i | \(-0.105441\pi\) | ||||
0.945635 | + | 0.325229i | \(0.105441\pi\) | |||||||
\(384\) | −2.81326 | −0.143564 | ||||||||
\(385\) | −5.92792 | −0.302115 | ||||||||
\(386\) | 5.25574 | 0.267510 | ||||||||
\(387\) | −10.4448 | −0.530940 | ||||||||
\(388\) | −10.1396 | −0.514759 | ||||||||
\(389\) | −19.9159 | −1.00978 | −0.504888 | − | 0.863185i | \(-0.668466\pi\) | ||||
−0.504888 | + | 0.863185i | \(0.668466\pi\) | |||||||
\(390\) | 5.36531 | 0.271683 | ||||||||
\(391\) | 16.9032 | 0.854831 | ||||||||
\(392\) | 8.41994 | 0.425271 | ||||||||
\(393\) | −61.4201 | −3.09824 | ||||||||
\(394\) | −8.47589 | −0.427009 | ||||||||
\(395\) | −2.84318 | −0.143056 | ||||||||
\(396\) | −10.1029 | −0.507690 | ||||||||
\(397\) | −23.8114 | −1.19506 | −0.597531 | − | 0.801846i | \(-0.703852\pi\) | ||||
−0.597531 | + | 0.801846i | \(0.703852\pi\) | |||||||
\(398\) | 18.1179 | 0.908166 | ||||||||
\(399\) | 27.3246 | 1.36794 | ||||||||
\(400\) | −4.46076 | −0.223038 | ||||||||
\(401\) | −2.70410 | −0.135036 | −0.0675182 | − | 0.997718i | \(-0.521508\pi\) | ||||
−0.0675182 | + | 0.997718i | \(0.521508\pi\) | |||||||
\(402\) | 0.0214000 | 0.00106733 | ||||||||
\(403\) | −16.0973 | −0.801863 | ||||||||
\(404\) | 9.52351 | 0.473812 | ||||||||
\(405\) | −0.299981 | −0.0149062 | ||||||||
\(406\) | 2.80411 | 0.139165 | ||||||||
\(407\) | −3.25371 | −0.161280 | ||||||||
\(408\) | 6.12932 | 0.303447 | ||||||||
\(409\) | 3.74277 | 0.185068 | 0.0925340 | − | 0.995710i | \(-0.470503\pi\) | ||||
0.0925340 | + | 0.995710i | \(0.470503\pi\) | |||||||
\(410\) | −0.865803 | −0.0427589 | ||||||||
\(411\) | 11.0461 | 0.544865 | ||||||||
\(412\) | −5.88240 | −0.289805 | ||||||||
\(413\) | 23.4664 | 1.15470 | ||||||||
\(414\) | −38.1278 | −1.87388 | ||||||||
\(415\) | 7.90801 | 0.388189 | ||||||||
\(416\) | 2.59713 | 0.127335 | ||||||||
\(417\) | 4.00227 | 0.195992 | ||||||||
\(418\) | −5.08479 | −0.248705 | ||||||||
\(419\) | −7.44839 | −0.363878 | −0.181939 | − | 0.983310i | \(-0.558237\pi\) | ||||
−0.181939 | + | 0.983310i | \(0.558237\pi\) | |||||||
\(420\) | −8.11226 | −0.395838 | ||||||||
\(421\) | 7.08079 | 0.345097 | 0.172548 | − | 0.985001i | \(-0.444800\pi\) | ||||
0.172548 | + | 0.985001i | \(0.444800\pi\) | |||||||
\(422\) | −2.84303 | −0.138396 | ||||||||
\(423\) | −30.2005 | −1.46840 | ||||||||
\(424\) | 7.69092 | 0.373504 | ||||||||
\(425\) | 9.71877 | 0.471429 | ||||||||
\(426\) | 34.9232 | 1.69204 | ||||||||
\(427\) | −34.0530 | −1.64794 | ||||||||
\(428\) | 3.55489 | 0.171832 | ||||||||
\(429\) | 15.0202 | 0.725183 | ||||||||
\(430\) | 1.56068 | 0.0752629 | ||||||||
\(431\) | −18.9658 | −0.913549 | −0.456775 | − | 0.889582i | \(-0.650995\pi\) | ||||
−0.456775 | + | 0.889582i | \(0.650995\pi\) | |||||||
\(432\) | −5.38587 | −0.259128 | ||||||||
\(433\) | 12.6446 | 0.607659 | 0.303829 | − | 0.952726i | \(-0.401735\pi\) | ||||
0.303829 | + | 0.952726i | \(0.401735\pi\) | |||||||
\(434\) | 24.3388 | 1.16830 | ||||||||
\(435\) | −1.47521 | −0.0707309 | ||||||||
\(436\) | −11.2797 | −0.540198 | ||||||||
\(437\) | −19.1897 | −0.917968 | ||||||||
\(438\) | 29.3677 | 1.40325 | ||||||||
\(439\) | −14.6445 | −0.698946 | −0.349473 | − | 0.936946i | \(-0.613639\pi\) | ||||
−0.349473 | + | 0.936946i | \(0.613639\pi\) | |||||||
\(440\) | 1.50960 | 0.0719672 | ||||||||
\(441\) | 41.3794 | 1.97045 | ||||||||
\(442\) | −5.65844 | −0.269144 | ||||||||
\(443\) | −11.1607 | −0.530260 | −0.265130 | − | 0.964213i | \(-0.585415\pi\) | ||||
−0.265130 | + | 0.964213i | \(0.585415\pi\) | |||||||
\(444\) | −4.45264 | −0.211313 | ||||||||
\(445\) | 2.75221 | 0.130467 | ||||||||
\(446\) | −19.1545 | −0.906991 | ||||||||
\(447\) | −50.5661 | −2.39169 | ||||||||
\(448\) | −3.92682 | −0.185525 | ||||||||
\(449\) | 18.8977 | 0.891837 | 0.445919 | − | 0.895073i | \(-0.352877\pi\) | ||||
0.445919 | + | 0.895073i | \(0.352877\pi\) | |||||||
\(450\) | −21.9222 | −1.03342 | ||||||||
\(451\) | −2.42382 | −0.114133 | ||||||||
\(452\) | 5.24049 | 0.246492 | ||||||||
\(453\) | 23.1906 | 1.08959 | ||||||||
\(454\) | 0.877514 | 0.0411838 | ||||||||
\(455\) | 7.48903 | 0.351091 | ||||||||
\(456\) | −6.95845 | −0.325859 | ||||||||
\(457\) | −15.1046 | −0.706564 | −0.353282 | − | 0.935517i | \(-0.614934\pi\) | ||||
−0.353282 | + | 0.935517i | \(0.614934\pi\) | |||||||
\(458\) | 27.2775 | 1.27459 | ||||||||
\(459\) | 11.7343 | 0.547711 | ||||||||
\(460\) | 5.69713 | 0.265630 | ||||||||
\(461\) | 19.7745 | 0.920992 | 0.460496 | − | 0.887662i | \(-0.347672\pi\) | ||||
0.460496 | + | 0.887662i | \(0.347672\pi\) | |||||||
\(462\) | −22.7103 | −1.05658 | ||||||||
\(463\) | −26.8959 | −1.24996 | −0.624980 | − | 0.780641i | \(-0.714893\pi\) | ||||
−0.624980 | + | 0.780641i | \(0.714893\pi\) | |||||||
\(464\) | −0.714090 | −0.0331508 | ||||||||
\(465\) | −12.8044 | −0.593789 | ||||||||
\(466\) | 4.79290 | 0.222027 | ||||||||
\(467\) | −3.15954 | −0.146206 | −0.0731030 | − | 0.997324i | \(-0.523290\pi\) | ||||
−0.0731030 | + | 0.997324i | \(0.523290\pi\) | |||||||
\(468\) | 12.7635 | 0.589993 | ||||||||
\(469\) | 0.0298706 | 0.00137930 | ||||||||
\(470\) | 4.51261 | 0.208151 | ||||||||
\(471\) | 11.0477 | 0.509050 | ||||||||
\(472\) | −5.97592 | −0.275064 | ||||||||
\(473\) | 4.36914 | 0.200893 | ||||||||
\(474\) | −10.8924 | −0.500305 | ||||||||
\(475\) | −11.0334 | −0.506249 | ||||||||
\(476\) | 8.55546 | 0.392139 | ||||||||
\(477\) | 37.7967 | 1.73059 | ||||||||
\(478\) | 14.2751 | 0.652927 | ||||||||
\(479\) | −2.96426 | −0.135441 | −0.0677203 | − | 0.997704i | \(-0.521573\pi\) | ||||
−0.0677203 | + | 0.997704i | \(0.521573\pi\) | |||||||
\(480\) | 2.06586 | 0.0942931 | ||||||||
\(481\) | 4.11057 | 0.187426 | ||||||||
\(482\) | 1.24232 | 0.0565861 | ||||||||
\(483\) | −85.7074 | −3.89982 | ||||||||
\(484\) | −6.77388 | −0.307904 | ||||||||
\(485\) | 7.44577 | 0.338095 | ||||||||
\(486\) | 15.0084 | 0.680793 | ||||||||
\(487\) | −3.17486 | −0.143867 | −0.0719334 | − | 0.997409i | \(-0.522917\pi\) | ||||
−0.0719334 | + | 0.997409i | \(0.522917\pi\) | |||||||
\(488\) | 8.67190 | 0.392558 | ||||||||
\(489\) | −48.8389 | −2.20857 | ||||||||
\(490\) | −6.18300 | −0.279319 | ||||||||
\(491\) | 8.43582 | 0.380703 | 0.190352 | − | 0.981716i | \(-0.439037\pi\) | ||||
0.190352 | + | 0.981716i | \(0.439037\pi\) | |||||||
\(492\) | −3.31695 | −0.149540 | ||||||||
\(493\) | 1.55580 | 0.0700699 | ||||||||
\(494\) | 6.42387 | 0.289023 | ||||||||
\(495\) | 7.41885 | 0.333452 | ||||||||
\(496\) | −6.19809 | −0.278303 | ||||||||
\(497\) | 48.7467 | 2.18659 | ||||||||
\(498\) | 30.2962 | 1.35760 | ||||||||
\(499\) | −27.6674 | −1.23856 | −0.619282 | − | 0.785169i | \(-0.712576\pi\) | ||||
−0.619282 | + | 0.785169i | \(0.712576\pi\) | |||||||
\(500\) | 6.94730 | 0.310693 | ||||||||
\(501\) | 9.69452 | 0.433119 | ||||||||
\(502\) | −21.9668 | −0.980426 | ||||||||
\(503\) | 5.84626 | 0.260672 | 0.130336 | − | 0.991470i | \(-0.458394\pi\) | ||||
0.130336 | + | 0.991470i | \(0.458394\pi\) | |||||||
\(504\) | −19.2982 | −0.859610 | ||||||||
\(505\) | −6.99337 | −0.311201 | ||||||||
\(506\) | 15.9491 | 0.709026 | ||||||||
\(507\) | 17.5967 | 0.781495 | ||||||||
\(508\) | −11.8477 | −0.525656 | ||||||||
\(509\) | −16.3150 | −0.723149 | −0.361575 | − | 0.932343i | \(-0.617761\pi\) | ||||
−0.361575 | + | 0.932343i | \(0.617761\pi\) | |||||||
\(510\) | −4.50093 | −0.199305 | ||||||||
\(511\) | 40.9922 | 1.81339 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −13.3216 | −0.588165 | ||||||||
\(514\) | 6.00777 | 0.264991 | ||||||||
\(515\) | 4.31961 | 0.190345 | ||||||||
\(516\) | 5.97910 | 0.263215 | ||||||||
\(517\) | 12.6331 | 0.555602 | ||||||||
\(518\) | −6.21511 | −0.273076 | ||||||||
\(519\) | 45.4644 | 1.99567 | ||||||||
\(520\) | −1.90715 | −0.0836340 | ||||||||
\(521\) | −13.3369 | −0.584301 | −0.292151 | − | 0.956372i | \(-0.594371\pi\) | ||||
−0.292151 | + | 0.956372i | \(0.594371\pi\) | |||||||
\(522\) | −3.50937 | −0.153601 | ||||||||
\(523\) | 21.4153 | 0.936426 | 0.468213 | − | 0.883616i | \(-0.344898\pi\) | ||||
0.468213 | + | 0.883616i | \(0.344898\pi\) | |||||||
\(524\) | 21.8323 | 0.953750 | ||||||||
\(525\) | −49.2789 | −2.15071 | ||||||||
\(526\) | 26.7329 | 1.16561 | ||||||||
\(527\) | 13.5039 | 0.588240 | ||||||||
\(528\) | 5.78338 | 0.251689 | ||||||||
\(529\) | 37.1912 | 1.61701 | ||||||||
\(530\) | −5.64766 | −0.245318 | ||||||||
\(531\) | −29.3684 | −1.27448 | ||||||||
\(532\) | −9.71277 | −0.421102 | ||||||||
\(533\) | 3.06213 | 0.132636 | ||||||||
\(534\) | 10.5439 | 0.456280 | ||||||||
\(535\) | −2.61045 | −0.112860 | ||||||||
\(536\) | −0.00760682 | −0.000328564 0 | ||||||||
\(537\) | −55.2197 | −2.38291 | ||||||||
\(538\) | −18.4790 | −0.796687 | ||||||||
\(539\) | −17.3093 | −0.745565 | ||||||||
\(540\) | 3.95499 | 0.170196 | ||||||||
\(541\) | 9.77628 | 0.420315 | 0.210158 | − | 0.977668i | \(-0.432602\pi\) | ||||
0.210158 | + | 0.977668i | \(0.432602\pi\) | |||||||
\(542\) | 27.7761 | 1.19308 | ||||||||
\(543\) | 29.0889 | 1.24832 | ||||||||
\(544\) | −2.17872 | −0.0934120 | ||||||||
\(545\) | 8.28298 | 0.354804 | ||||||||
\(546\) | 28.6910 | 1.22786 | ||||||||
\(547\) | −15.8470 | −0.677567 | −0.338783 | − | 0.940864i | \(-0.610015\pi\) | ||||
−0.338783 | + | 0.940864i | \(0.610015\pi\) | |||||||
\(548\) | −3.92644 | −0.167729 | ||||||||
\(549\) | 42.6177 | 1.81888 | ||||||||
\(550\) | 9.17023 | 0.391020 | ||||||||
\(551\) | −1.76626 | −0.0752453 | ||||||||
\(552\) | 21.8261 | 0.928982 | ||||||||
\(553\) | −15.2039 | −0.646536 | ||||||||
\(554\) | −8.76025 | −0.372187 | ||||||||
\(555\) | 3.26970 | 0.138791 | ||||||||
\(556\) | −1.42264 | −0.0603335 | ||||||||
\(557\) | 7.25698 | 0.307488 | 0.153744 | − | 0.988111i | \(-0.450867\pi\) | ||||
0.153744 | + | 0.988111i | \(0.450867\pi\) | |||||||
\(558\) | −30.4603 | −1.28949 | ||||||||
\(559\) | −5.51975 | −0.233461 | ||||||||
\(560\) | 2.88358 | 0.121853 | ||||||||
\(561\) | −12.6004 | −0.531988 | ||||||||
\(562\) | 24.5807 | 1.03687 | ||||||||
\(563\) | −0.800106 | −0.0337204 | −0.0168602 | − | 0.999858i | \(-0.505367\pi\) | ||||
−0.0168602 | + | 0.999858i | \(0.505367\pi\) | |||||||
\(564\) | 17.2882 | 0.727963 | ||||||||
\(565\) | −3.84824 | −0.161896 | ||||||||
\(566\) | 11.9549 | 0.502502 | ||||||||
\(567\) | −1.60415 | −0.0673681 | ||||||||
\(568\) | −12.4138 | −0.520871 | ||||||||
\(569\) | −18.6311 | −0.781056 | −0.390528 | − | 0.920591i | \(-0.627707\pi\) | ||||
−0.390528 | + | 0.920591i | \(0.627707\pi\) | |||||||
\(570\) | 5.10978 | 0.214025 | ||||||||
\(571\) | 21.9283 | 0.917672 | 0.458836 | − | 0.888521i | \(-0.348266\pi\) | ||||
0.458836 | + | 0.888521i | \(0.348266\pi\) | |||||||
\(572\) | −5.33907 | −0.223238 | ||||||||
\(573\) | −49.4489 | −2.06576 | ||||||||
\(574\) | −4.62989 | −0.193248 | ||||||||
\(575\) | 34.6079 | 1.44325 | ||||||||
\(576\) | 4.91446 | 0.204769 | ||||||||
\(577\) | 9.80941 | 0.408371 | 0.204186 | − | 0.978932i | \(-0.434545\pi\) | ||||
0.204186 | + | 0.978932i | \(0.434545\pi\) | |||||||
\(578\) | −12.2532 | −0.509665 | ||||||||
\(579\) | −14.7858 | −0.614476 | ||||||||
\(580\) | 0.524376 | 0.0217735 | ||||||||
\(581\) | 42.2882 | 1.75441 | ||||||||
\(582\) | 28.5253 | 1.18241 | ||||||||
\(583\) | −15.8106 | −0.654810 | ||||||||
\(584\) | −10.4390 | −0.431970 | ||||||||
\(585\) | −9.37260 | −0.387509 | ||||||||
\(586\) | 16.6317 | 0.687051 | ||||||||
\(587\) | 8.51631 | 0.351506 | 0.175753 | − | 0.984434i | \(-0.443764\pi\) | ||||
0.175753 | + | 0.984434i | \(0.443764\pi\) | |||||||
\(588\) | −23.6875 | −0.976857 | ||||||||
\(589\) | −15.3306 | −0.631688 | ||||||||
\(590\) | 4.38828 | 0.180663 | ||||||||
\(591\) | 23.8449 | 0.980849 | ||||||||
\(592\) | 1.58273 | 0.0650499 | ||||||||
\(593\) | 4.40968 | 0.181084 | 0.0905420 | − | 0.995893i | \(-0.471140\pi\) | ||||
0.0905420 | + | 0.995893i | \(0.471140\pi\) | |||||||
\(594\) | 11.0720 | 0.454291 | ||||||||
\(595\) | −6.28251 | −0.257558 | ||||||||
\(596\) | 17.9742 | 0.736250 | ||||||||
\(597\) | −50.9703 | −2.08608 | ||||||||
\(598\) | −20.1493 | −0.823968 | ||||||||
\(599\) | 20.9772 | 0.857104 | 0.428552 | − | 0.903517i | \(-0.359024\pi\) | ||||
0.428552 | + | 0.903517i | \(0.359024\pi\) | |||||||
\(600\) | 12.5493 | 0.512323 | ||||||||
\(601\) | −6.26787 | −0.255672 | −0.127836 | − | 0.991795i | \(-0.540803\pi\) | ||||
−0.127836 | + | 0.991795i | \(0.540803\pi\) | |||||||
\(602\) | 8.34577 | 0.340148 | ||||||||
\(603\) | −0.0373834 | −0.00152237 | ||||||||
\(604\) | −8.24330 | −0.335415 | ||||||||
\(605\) | 4.97425 | 0.202232 | ||||||||
\(606\) | −26.7921 | −1.08836 | ||||||||
\(607\) | −6.78717 | −0.275483 | −0.137741 | − | 0.990468i | \(-0.543984\pi\) | ||||
−0.137741 | + | 0.990468i | \(0.543984\pi\) | |||||||
\(608\) | 2.47344 | 0.100311 | ||||||||
\(609\) | −7.88869 | −0.319666 | ||||||||
\(610\) | −6.36802 | −0.257833 | ||||||||
\(611\) | −15.9600 | −0.645672 | ||||||||
\(612\) | −10.7072 | −0.432814 | ||||||||
\(613\) | 22.9234 | 0.925866 | 0.462933 | − | 0.886393i | \(-0.346797\pi\) | ||||
0.462933 | + | 0.886393i | \(0.346797\pi\) | |||||||
\(614\) | 26.9050 | 1.08580 | ||||||||
\(615\) | 2.43573 | 0.0982182 | ||||||||
\(616\) | 8.07258 | 0.325254 | ||||||||
\(617\) | 5.57814 | 0.224568 | 0.112284 | − | 0.993676i | \(-0.464183\pi\) | ||||
0.112284 | + | 0.993676i | \(0.464183\pi\) | |||||||
\(618\) | 16.5487 | 0.665688 | ||||||||
\(619\) | −2.37216 | −0.0953451 | −0.0476726 | − | 0.998863i | \(-0.515180\pi\) | ||||
−0.0476726 | + | 0.998863i | \(0.515180\pi\) | |||||||
\(620\) | 4.55143 | 0.182790 | ||||||||
\(621\) | 41.7852 | 1.67678 | ||||||||
\(622\) | 22.3242 | 0.895117 | ||||||||
\(623\) | 14.7175 | 0.589643 | ||||||||
\(624\) | −7.30643 | −0.292491 | ||||||||
\(625\) | 17.2022 | 0.688089 | ||||||||
\(626\) | 22.4422 | 0.896971 | ||||||||
\(627\) | 14.3049 | 0.571281 | ||||||||
\(628\) | −3.92699 | −0.156704 | ||||||||
\(629\) | −3.44833 | −0.137494 | ||||||||
\(630\) | 14.1712 | 0.564594 | ||||||||
\(631\) | −8.02213 | −0.319356 | −0.159678 | − | 0.987169i | \(-0.551046\pi\) | ||||
−0.159678 | + | 0.987169i | \(0.551046\pi\) | |||||||
\(632\) | 3.87181 | 0.154012 | ||||||||
\(633\) | 7.99819 | 0.317899 | ||||||||
\(634\) | 3.53246 | 0.140292 | ||||||||
\(635\) | 8.70008 | 0.345252 | ||||||||
\(636\) | −21.6366 | −0.857947 | ||||||||
\(637\) | 21.8677 | 0.866430 | ||||||||
\(638\) | 1.46799 | 0.0581184 | ||||||||
\(639\) | −61.0070 | −2.41340 | ||||||||
\(640\) | −0.734328 | −0.0290269 | ||||||||
\(641\) | 5.33448 | 0.210699 | 0.105350 | − | 0.994435i | \(-0.466404\pi\) | ||||
0.105350 | + | 0.994435i | \(0.466404\pi\) | |||||||
\(642\) | −10.0008 | −0.394701 | ||||||||
\(643\) | −39.1058 | −1.54218 | −0.771091 | − | 0.636725i | \(-0.780289\pi\) | ||||
−0.771091 | + | 0.636725i | \(0.780289\pi\) | |||||||
\(644\) | 30.4655 | 1.20051 | ||||||||
\(645\) | −4.39062 | −0.172880 | ||||||||
\(646\) | −5.38895 | −0.212025 | ||||||||
\(647\) | −27.0401 | −1.06306 | −0.531528 | − | 0.847041i | \(-0.678382\pi\) | ||||
−0.531528 | + | 0.847041i | \(0.678382\pi\) | |||||||
\(648\) | 0.408511 | 0.0160478 | ||||||||
\(649\) | 12.2850 | 0.482229 | ||||||||
\(650\) | −11.5852 | −0.454409 | ||||||||
\(651\) | −68.4715 | −2.68361 | ||||||||
\(652\) | 17.3602 | 0.679878 | ||||||||
\(653\) | −32.6892 | −1.27923 | −0.639613 | − | 0.768697i | \(-0.720905\pi\) | ||||
−0.639613 | + | 0.768697i | \(0.720905\pi\) | |||||||
\(654\) | 31.7327 | 1.24085 | ||||||||
\(655\) | −16.0321 | −0.626426 | ||||||||
\(656\) | 1.17904 | 0.0460338 | ||||||||
\(657\) | −51.3022 | −2.00149 | ||||||||
\(658\) | 24.1312 | 0.940734 | ||||||||
\(659\) | 22.2631 | 0.867248 | 0.433624 | − | 0.901094i | \(-0.357235\pi\) | ||||
0.433624 | + | 0.901094i | \(0.357235\pi\) | |||||||
\(660\) | −4.24689 | −0.165310 | ||||||||
\(661\) | 21.0608 | 0.819169 | 0.409584 | − | 0.912272i | \(-0.365674\pi\) | ||||
0.409584 | + | 0.912272i | \(0.365674\pi\) | |||||||
\(662\) | 2.89771 | 0.112623 | ||||||||
\(663\) | 15.9187 | 0.618230 | ||||||||
\(664\) | −10.7691 | −0.417920 | ||||||||
\(665\) | 7.13236 | 0.276581 | ||||||||
\(666\) | 7.77826 | 0.301402 | ||||||||
\(667\) | 5.54013 | 0.214515 | ||||||||
\(668\) | −3.44601 | −0.133330 | ||||||||
\(669\) | 53.8866 | 2.08338 | ||||||||
\(670\) | 0.00558590 | 0.000215802 0 | ||||||||
\(671\) | −17.8273 | −0.688215 | ||||||||
\(672\) | 11.0472 | 0.426155 | ||||||||
\(673\) | −1.31532 | −0.0507020 | −0.0253510 | − | 0.999679i | \(-0.508070\pi\) | ||||
−0.0253510 | + | 0.999679i | \(0.508070\pi\) | |||||||
\(674\) | 20.0941 | 0.773997 | ||||||||
\(675\) | 24.0251 | 0.924726 | ||||||||
\(676\) | −6.25489 | −0.240573 | ||||||||
\(677\) | 27.9736 | 1.07511 | 0.537556 | − | 0.843228i | \(-0.319347\pi\) | ||||
0.537556 | + | 0.843228i | \(0.319347\pi\) | |||||||
\(678\) | −14.7429 | −0.566197 | ||||||||
\(679\) | 39.8163 | 1.52801 | ||||||||
\(680\) | 1.59990 | 0.0613532 | ||||||||
\(681\) | −2.46868 | −0.0946000 | ||||||||
\(682\) | 12.7418 | 0.487907 | ||||||||
\(683\) | −18.5127 | −0.708369 | −0.354184 | − | 0.935176i | \(-0.615242\pi\) | ||||
−0.354184 | + | 0.935176i | \(0.615242\pi\) | |||||||
\(684\) | 12.1556 | 0.464782 | ||||||||
\(685\) | 2.88329 | 0.110165 | ||||||||
\(686\) | −5.57585 | −0.212887 | ||||||||
\(687\) | −76.7387 | −2.92776 | ||||||||
\(688\) | −2.12532 | −0.0810272 | ||||||||
\(689\) | 19.9744 | 0.760962 | ||||||||
\(690\) | −16.0275 | −0.610158 | ||||||||
\(691\) | 21.3616 | 0.812633 | 0.406317 | − | 0.913732i | \(-0.366813\pi\) | ||||
0.406317 | + | 0.913732i | \(0.366813\pi\) | |||||||
\(692\) | −16.1607 | −0.614339 | ||||||||
\(693\) | 39.6723 | 1.50703 | ||||||||
\(694\) | −4.72179 | −0.179237 | ||||||||
\(695\) | 1.04469 | 0.0396272 | ||||||||
\(696\) | 2.00892 | 0.0761481 | ||||||||
\(697\) | −2.56880 | −0.0973004 | ||||||||
\(698\) | 30.4172 | 1.15131 | ||||||||
\(699\) | −13.4837 | −0.510000 | ||||||||
\(700\) | 17.5166 | 0.662066 | ||||||||
\(701\) | 4.93440 | 0.186370 | 0.0931849 | − | 0.995649i | \(-0.470295\pi\) | ||||
0.0931849 | + | 0.995649i | \(0.470295\pi\) | |||||||
\(702\) | −13.9878 | −0.527937 | ||||||||
\(703\) | 3.91480 | 0.147649 | ||||||||
\(704\) | −2.05575 | −0.0774791 | ||||||||
\(705\) | −12.6952 | −0.478128 | ||||||||
\(706\) | 18.0228 | 0.678298 | ||||||||
\(707\) | −37.3971 | −1.40646 | ||||||||
\(708\) | 16.8118 | 0.631827 | ||||||||
\(709\) | −9.37610 | −0.352127 | −0.176063 | − | 0.984379i | \(-0.556336\pi\) | ||||
−0.176063 | + | 0.984379i | \(0.556336\pi\) | |||||||
\(710\) | 9.11578 | 0.342109 | ||||||||
\(711\) | 19.0278 | 0.713599 | ||||||||
\(712\) | −3.74793 | −0.140460 | ||||||||
\(713\) | 48.0867 | 1.80086 | ||||||||
\(714\) | −24.0688 | −0.900751 | ||||||||
\(715\) | 3.92063 | 0.146623 | ||||||||
\(716\) | 19.6283 | 0.733545 | ||||||||
\(717\) | −40.1596 | −1.49979 | ||||||||
\(718\) | −9.99489 | −0.373006 | ||||||||
\(719\) | −14.3531 | −0.535281 | −0.267641 | − | 0.963519i | \(-0.586244\pi\) | ||||
−0.267641 | + | 0.963519i | \(0.586244\pi\) | |||||||
\(720\) | −3.60882 | −0.134493 | ||||||||
\(721\) | 23.0991 | 0.860257 | ||||||||
\(722\) | −12.8821 | −0.479421 | ||||||||
\(723\) | −3.49497 | −0.129979 | ||||||||
\(724\) | −10.3399 | −0.384280 | ||||||||
\(725\) | 3.18539 | 0.118302 | ||||||||
\(726\) | 19.0567 | 0.707261 | ||||||||
\(727\) | 10.3382 | 0.383423 | 0.191711 | − | 0.981451i | \(-0.438596\pi\) | ||||
0.191711 | + | 0.981451i | \(0.438596\pi\) | |||||||
\(728\) | −10.1985 | −0.377981 | ||||||||
\(729\) | −43.4480 | −1.60919 | ||||||||
\(730\) | 7.66567 | 0.283719 | ||||||||
\(731\) | 4.63049 | 0.171265 | ||||||||
\(732\) | −24.3963 | −0.901715 | ||||||||
\(733\) | −2.11447 | −0.0780997 | −0.0390499 | − | 0.999237i | \(-0.512433\pi\) | ||||
−0.0390499 | + | 0.999237i | \(0.512433\pi\) | |||||||
\(734\) | 4.60952 | 0.170140 | ||||||||
\(735\) | 17.3944 | 0.641602 | ||||||||
\(736\) | −7.75830 | −0.285975 | ||||||||
\(737\) | 0.0156377 | 0.000576024 0 | ||||||||
\(738\) | 5.79435 | 0.213293 | ||||||||
\(739\) | −30.1519 | −1.10916 | −0.554579 | − | 0.832131i | \(-0.687121\pi\) | ||||
−0.554579 | + | 0.832131i | \(0.687121\pi\) | |||||||
\(740\) | −1.16224 | −0.0427249 | ||||||||
\(741\) | −18.0720 | −0.663893 | ||||||||
\(742\) | −30.2009 | −1.10871 | ||||||||
\(743\) | 9.93168 | 0.364358 | 0.182179 | − | 0.983265i | \(-0.441685\pi\) | ||||
0.182179 | + | 0.983265i | \(0.441685\pi\) | |||||||
\(744\) | 17.4369 | 0.639267 | ||||||||
\(745\) | −13.1989 | −0.483571 | ||||||||
\(746\) | −28.6127 | −1.04758 | ||||||||
\(747\) | −52.9240 | −1.93639 | ||||||||
\(748\) | 4.47892 | 0.163765 | ||||||||
\(749\) | −13.9594 | −0.510066 | ||||||||
\(750\) | −19.5446 | −0.713668 | ||||||||
\(751\) | −15.3722 | −0.560939 | −0.280470 | − | 0.959863i | \(-0.590490\pi\) | ||||
−0.280470 | + | 0.959863i | \(0.590490\pi\) | |||||||
\(752\) | −6.14523 | −0.224094 | ||||||||
\(753\) | 61.7984 | 2.25206 | ||||||||
\(754\) | −1.85459 | −0.0675401 | ||||||||
\(755\) | 6.05328 | 0.220302 | ||||||||
\(756\) | 21.1494 | 0.769195 | ||||||||
\(757\) | −15.4552 | −0.561729 | −0.280864 | − | 0.959747i | \(-0.590621\pi\) | ||||
−0.280864 | + | 0.959747i | \(0.590621\pi\) | |||||||
\(758\) | −21.0909 | −0.766057 | ||||||||
\(759\) | −44.8692 | −1.62865 | ||||||||
\(760\) | −1.81632 | −0.0658848 | ||||||||
\(761\) | 12.7408 | 0.461853 | 0.230927 | − | 0.972971i | \(-0.425824\pi\) | ||||
0.230927 | + | 0.972971i | \(0.425824\pi\) | |||||||
\(762\) | 33.3307 | 1.20744 | ||||||||
\(763\) | 44.2933 | 1.60352 | ||||||||
\(764\) | 17.5770 | 0.635915 | ||||||||
\(765\) | 7.86262 | 0.284274 | ||||||||
\(766\) | 37.0129 | 1.33733 | ||||||||
\(767\) | −15.5203 | −0.560404 | ||||||||
\(768\) | −2.81326 | −0.101515 | ||||||||
\(769\) | 46.2554 | 1.66801 | 0.834007 | − | 0.551754i | \(-0.186041\pi\) | ||||
0.834007 | + | 0.551754i | \(0.186041\pi\) | |||||||
\(770\) | −5.92792 | −0.213627 | ||||||||
\(771\) | −16.9014 | −0.608691 | ||||||||
\(772\) | 5.25574 | 0.189158 | ||||||||
\(773\) | 32.7888 | 1.17933 | 0.589666 | − | 0.807647i | \(-0.299260\pi\) | ||||
0.589666 | + | 0.807647i | \(0.299260\pi\) | |||||||
\(774\) | −10.4448 | −0.375431 | ||||||||
\(775\) | 27.6482 | 0.993153 | ||||||||
\(776\) | −10.1396 | −0.363990 | ||||||||
\(777\) | 17.4847 | 0.627261 | ||||||||
\(778\) | −19.9159 | −0.714019 | ||||||||
\(779\) | 2.91629 | 0.104487 | ||||||||
\(780\) | 5.36531 | 0.192109 | ||||||||
\(781\) | 25.5197 | 0.913166 | ||||||||
\(782\) | 16.9032 | 0.604457 | ||||||||
\(783\) | 3.84600 | 0.137445 | ||||||||
\(784\) | 8.41994 | 0.300712 | ||||||||
\(785\) | 2.88370 | 0.102924 | ||||||||
\(786\) | −61.4201 | −2.19078 | ||||||||
\(787\) | 31.8370 | 1.13487 | 0.567433 | − | 0.823420i | \(-0.307937\pi\) | ||||
0.567433 | + | 0.823420i | \(0.307937\pi\) | |||||||
\(788\) | −8.47589 | −0.301941 | ||||||||
\(789\) | −75.2068 | −2.67743 | ||||||||
\(790\) | −2.84318 | −0.101156 | ||||||||
\(791\) | −20.5785 | −0.731686 | ||||||||
\(792\) | −10.1029 | −0.358991 | ||||||||
\(793\) | 22.5221 | 0.799783 | ||||||||
\(794\) | −23.8114 | −0.845037 | ||||||||
\(795\) | 15.8883 | 0.563502 | ||||||||
\(796\) | 18.1179 | 0.642171 | ||||||||
\(797\) | −11.4111 | −0.404203 | −0.202101 | − | 0.979365i | \(-0.564777\pi\) | ||||
−0.202101 | + | 0.979365i | \(0.564777\pi\) | |||||||
\(798\) | 27.3246 | 0.967280 | ||||||||
\(799\) | 13.3888 | 0.473660 | ||||||||
\(800\) | −4.46076 | −0.157712 | ||||||||
\(801\) | −18.4191 | −0.650805 | ||||||||
\(802\) | −2.70410 | −0.0954852 | ||||||||
\(803\) | 21.4601 | 0.757309 | ||||||||
\(804\) | 0.0214000 | 0.000754719 0 | ||||||||
\(805\) | −22.3716 | −0.788497 | ||||||||
\(806\) | −16.0973 | −0.567003 | ||||||||
\(807\) | 51.9863 | 1.83001 | ||||||||
\(808\) | 9.52351 | 0.335036 | ||||||||
\(809\) | −32.3923 | −1.13885 | −0.569426 | − | 0.822042i | \(-0.692835\pi\) | ||||
−0.569426 | + | 0.822042i | \(0.692835\pi\) | |||||||
\(810\) | −0.299981 | −0.0105403 | ||||||||
\(811\) | 23.8988 | 0.839199 | 0.419599 | − | 0.907709i | \(-0.362171\pi\) | ||||
0.419599 | + | 0.907709i | \(0.362171\pi\) | |||||||
\(812\) | 2.80411 | 0.0984048 | ||||||||
\(813\) | −78.1414 | −2.74054 | ||||||||
\(814\) | −3.25371 | −0.114042 | ||||||||
\(815\) | −12.7481 | −0.446546 | ||||||||
\(816\) | 6.12932 | 0.214569 | ||||||||
\(817\) | −5.25687 | −0.183915 | ||||||||
\(818\) | 3.74277 | 0.130863 | ||||||||
\(819\) | −50.1200 | −1.75134 | ||||||||
\(820\) | −0.865803 | −0.0302351 | ||||||||
\(821\) | 13.0773 | 0.456402 | 0.228201 | − | 0.973614i | \(-0.426716\pi\) | ||||
0.228201 | + | 0.973614i | \(0.426716\pi\) | |||||||
\(822\) | 11.0461 | 0.385278 | ||||||||
\(823\) | 16.9076 | 0.589361 | 0.294680 | − | 0.955596i | \(-0.404787\pi\) | ||||
0.294680 | + | 0.955596i | \(0.404787\pi\) | |||||||
\(824\) | −5.88240 | −0.204923 | ||||||||
\(825\) | −25.7983 | −0.898181 | ||||||||
\(826\) | 23.4664 | 0.816499 | ||||||||
\(827\) | 1.68620 | 0.0586349 | 0.0293175 | − | 0.999570i | \(-0.490667\pi\) | ||||
0.0293175 | + | 0.999570i | \(0.490667\pi\) | |||||||
\(828\) | −38.1278 | −1.32503 | ||||||||
\(829\) | −1.16499 | −0.0404619 | −0.0202309 | − | 0.999795i | \(-0.506440\pi\) | ||||
−0.0202309 | + | 0.999795i | \(0.506440\pi\) | |||||||
\(830\) | 7.90801 | 0.274491 | ||||||||
\(831\) | 24.6449 | 0.854922 | ||||||||
\(832\) | 2.59713 | 0.0900394 | ||||||||
\(833\) | −18.3447 | −0.635607 | ||||||||
\(834\) | 4.00227 | 0.138587 | ||||||||
\(835\) | 2.53050 | 0.0875715 | ||||||||
\(836\) | −5.08479 | −0.175861 | ||||||||
\(837\) | 33.3821 | 1.15386 | ||||||||
\(838\) | −7.44839 | −0.257300 | ||||||||
\(839\) | 40.0136 | 1.38142 | 0.690712 | − | 0.723130i | \(-0.257297\pi\) | ||||
0.690712 | + | 0.723130i | \(0.257297\pi\) | |||||||
\(840\) | −8.11226 | −0.279900 | ||||||||
\(841\) | −28.4901 | −0.982416 | ||||||||
\(842\) | 7.08079 | 0.244020 | ||||||||
\(843\) | −69.1520 | −2.38172 | ||||||||
\(844\) | −2.84303 | −0.0978610 | ||||||||
\(845\) | 4.59314 | 0.158009 | ||||||||
\(846\) | −30.2005 | −1.03831 | ||||||||
\(847\) | 26.5998 | 0.913981 | ||||||||
\(848\) | 7.69092 | 0.264107 | ||||||||
\(849\) | −33.6323 | −1.15426 | ||||||||
\(850\) | 9.71877 | 0.333351 | ||||||||
\(851\) | −12.2793 | −0.420929 | ||||||||
\(852\) | 34.9232 | 1.19645 | ||||||||
\(853\) | 18.1409 | 0.621133 | 0.310567 | − | 0.950552i | \(-0.399481\pi\) | ||||
0.310567 | + | 0.950552i | \(0.399481\pi\) | |||||||
\(854\) | −34.0530 | −1.16527 | ||||||||
\(855\) | −8.92622 | −0.305270 | ||||||||
\(856\) | 3.55489 | 0.121504 | ||||||||
\(857\) | −54.0968 | −1.84791 | −0.923956 | − | 0.382499i | \(-0.875064\pi\) | ||||
−0.923956 | + | 0.382499i | \(0.875064\pi\) | |||||||
\(858\) | 15.0202 | 0.512782 | ||||||||
\(859\) | −36.7088 | −1.25249 | −0.626245 | − | 0.779627i | \(-0.715409\pi\) | ||||
−0.626245 | + | 0.779627i | \(0.715409\pi\) | |||||||
\(860\) | 1.56068 | 0.0532189 | ||||||||
\(861\) | 13.0251 | 0.443894 | ||||||||
\(862\) | −18.9658 | −0.645977 | ||||||||
\(863\) | −42.2917 | −1.43963 | −0.719814 | − | 0.694167i | \(-0.755773\pi\) | ||||
−0.719814 | + | 0.694167i | \(0.755773\pi\) | |||||||
\(864\) | −5.38587 | −0.183231 | ||||||||
\(865\) | 11.8673 | 0.403500 | ||||||||
\(866\) | 12.6446 | 0.429680 | ||||||||
\(867\) | 34.4714 | 1.17071 | ||||||||
\(868\) | 24.3388 | 0.826113 | ||||||||
\(869\) | −7.95948 | −0.270007 | ||||||||
\(870\) | −1.47521 | −0.0500143 | ||||||||
\(871\) | −0.0197559 | −0.000669404 0 | ||||||||
\(872\) | −11.2797 | −0.381978 | ||||||||
\(873\) | −49.8305 | −1.68651 | ||||||||
\(874\) | −19.1897 | −0.649102 | ||||||||
\(875\) | −27.2808 | −0.922260 | ||||||||
\(876\) | 29.3677 | 0.992244 | ||||||||
\(877\) | −29.1695 | −0.984983 | −0.492492 | − | 0.870317i | \(-0.663914\pi\) | ||||
−0.492492 | + | 0.870317i | \(0.663914\pi\) | |||||||
\(878\) | −14.6445 | −0.494230 | ||||||||
\(879\) | −46.7895 | −1.57817 | ||||||||
\(880\) | 1.50960 | 0.0508885 | ||||||||
\(881\) | 8.74845 | 0.294743 | 0.147371 | − | 0.989081i | \(-0.452919\pi\) | ||||
0.147371 | + | 0.989081i | \(0.452919\pi\) | |||||||
\(882\) | 41.3794 | 1.39332 | ||||||||
\(883\) | −30.6262 | −1.03065 | −0.515326 | − | 0.856994i | \(-0.672329\pi\) | ||||
−0.515326 | + | 0.856994i | \(0.672329\pi\) | |||||||
\(884\) | −5.65844 | −0.190314 | ||||||||
\(885\) | −12.3454 | −0.414986 | ||||||||
\(886\) | −11.1607 | −0.374951 | ||||||||
\(887\) | −1.80985 | −0.0607689 | −0.0303845 | − | 0.999538i | \(-0.509673\pi\) | ||||
−0.0303845 | + | 0.999538i | \(0.509673\pi\) | |||||||
\(888\) | −4.45264 | −0.149421 | ||||||||
\(889\) | 46.5238 | 1.56036 | ||||||||
\(890\) | 2.75221 | 0.0922543 | ||||||||
\(891\) | −0.839799 | −0.0281343 | ||||||||
\(892\) | −19.1545 | −0.641339 | ||||||||
\(893\) | −15.1999 | −0.508645 | ||||||||
\(894\) | −50.5661 | −1.69118 | ||||||||
\(895\) | −14.4136 | −0.481794 | ||||||||
\(896\) | −3.92682 | −0.131186 | ||||||||
\(897\) | 56.6854 | 1.89267 | ||||||||
\(898\) | 18.8977 | 0.630624 | ||||||||
\(899\) | 4.42600 | 0.147615 | ||||||||
\(900\) | −21.9222 | −0.730741 | ||||||||
\(901\) | −16.7564 | −0.558236 | ||||||||
\(902\) | −2.42382 | −0.0807043 | ||||||||
\(903\) | −23.4789 | −0.781328 | ||||||||
\(904\) | 5.24049 | 0.174296 | ||||||||
\(905\) | 7.59288 | 0.252396 | ||||||||
\(906\) | 23.1906 | 0.770456 | ||||||||
\(907\) | −50.9199 | −1.69077 | −0.845383 | − | 0.534160i | \(-0.820628\pi\) | ||||
−0.845383 | + | 0.534160i | \(0.820628\pi\) | |||||||
\(908\) | 0.877514 | 0.0291213 | ||||||||
\(909\) | 46.8029 | 1.55235 | ||||||||
\(910\) | 7.48903 | 0.248259 | ||||||||
\(911\) | −12.1154 | −0.401400 | −0.200700 | − | 0.979653i | \(-0.564322\pi\) | ||||
−0.200700 | + | 0.979653i | \(0.564322\pi\) | |||||||
\(912\) | −6.95845 | −0.230417 | ||||||||
\(913\) | 22.1385 | 0.732678 | ||||||||
\(914\) | −15.1046 | −0.499616 | ||||||||
\(915\) | 17.9149 | 0.592249 | ||||||||
\(916\) | 27.2775 | 0.901273 | ||||||||
\(917\) | −85.7317 | −2.83111 | ||||||||
\(918\) | 11.7343 | 0.387290 | ||||||||
\(919\) | 9.90729 | 0.326811 | 0.163406 | − | 0.986559i | \(-0.447752\pi\) | ||||
0.163406 | + | 0.986559i | \(0.447752\pi\) | |||||||
\(920\) | 5.69713 | 0.187829 | ||||||||
\(921\) | −75.6908 | −2.49410 | ||||||||
\(922\) | 19.7745 | 0.651239 | ||||||||
\(923\) | −32.2403 | −1.06120 | ||||||||
\(924\) | −22.7103 | −0.747114 | ||||||||
\(925\) | −7.06019 | −0.232138 | ||||||||
\(926\) | −26.8959 | −0.883855 | ||||||||
\(927\) | −28.9088 | −0.949489 | ||||||||
\(928\) | −0.714090 | −0.0234412 | ||||||||
\(929\) | 26.0654 | 0.855176 | 0.427588 | − | 0.903974i | \(-0.359363\pi\) | ||||
0.427588 | + | 0.903974i | \(0.359363\pi\) | |||||||
\(930\) | −12.8044 | −0.419872 | ||||||||
\(931\) | 20.8262 | 0.682553 | ||||||||
\(932\) | 4.79290 | 0.156997 | ||||||||
\(933\) | −62.8038 | −2.05610 | ||||||||
\(934\) | −3.15954 | −0.103383 | ||||||||
\(935\) | −3.28899 | −0.107562 | ||||||||
\(936\) | 12.7635 | 0.417188 | ||||||||
\(937\) | 2.90578 | 0.0949276 | 0.0474638 | − | 0.998873i | \(-0.484886\pi\) | ||||
0.0474638 | + | 0.998873i | \(0.484886\pi\) | |||||||
\(938\) | 0.0298706 | 0.000975310 0 | ||||||||
\(939\) | −63.1359 | −2.06036 | ||||||||
\(940\) | 4.51261 | 0.147185 | ||||||||
\(941\) | −31.7213 | −1.03408 | −0.517042 | − | 0.855960i | \(-0.672967\pi\) | ||||
−0.517042 | + | 0.855960i | \(0.672967\pi\) | |||||||
\(942\) | 11.0477 | 0.359953 | ||||||||
\(943\) | −9.14735 | −0.297879 | ||||||||
\(944\) | −5.97592 | −0.194500 | ||||||||
\(945\) | −15.5306 | −0.505209 | ||||||||
\(946\) | 4.36914 | 0.142053 | ||||||||
\(947\) | 45.7267 | 1.48592 | 0.742960 | − | 0.669336i | \(-0.233421\pi\) | ||||
0.742960 | + | 0.669336i | \(0.233421\pi\) | |||||||
\(948\) | −10.8924 | −0.353769 | ||||||||
\(949\) | −27.1116 | −0.880079 | ||||||||
\(950\) | −11.0334 | −0.357972 | ||||||||
\(951\) | −9.93775 | −0.322254 | ||||||||
\(952\) | 8.55546 | 0.277284 | ||||||||
\(953\) | 10.0534 | 0.325663 | 0.162832 | − | 0.986654i | \(-0.447937\pi\) | ||||
0.162832 | + | 0.986654i | \(0.447937\pi\) | |||||||
\(954\) | 37.7967 | 1.22371 | ||||||||
\(955\) | −12.9073 | −0.417671 | ||||||||
\(956\) | 14.2751 | 0.461689 | ||||||||
\(957\) | −4.12985 | −0.133499 | ||||||||
\(958\) | −2.96426 | −0.0957710 | ||||||||
\(959\) | 15.4184 | 0.497887 | ||||||||
\(960\) | 2.06586 | 0.0666753 | ||||||||
\(961\) | 7.41636 | 0.239237 | ||||||||
\(962\) | 4.11057 | 0.132530 | ||||||||
\(963\) | 17.4703 | 0.562974 | ||||||||
\(964\) | 1.24232 | 0.0400124 | ||||||||
\(965\) | −3.85943 | −0.124240 | ||||||||
\(966\) | −85.7074 | −2.75759 | ||||||||
\(967\) | −60.1519 | −1.93436 | −0.967178 | − | 0.254099i | \(-0.918221\pi\) | ||||
−0.967178 | + | 0.254099i | \(0.918221\pi\) | |||||||
\(968\) | −6.77388 | −0.217721 | ||||||||
\(969\) | 15.1605 | 0.487027 | ||||||||
\(970\) | 7.44577 | 0.239069 | ||||||||
\(971\) | 24.3630 | 0.781847 | 0.390923 | − | 0.920423i | \(-0.372156\pi\) | ||||
0.390923 | + | 0.920423i | \(0.372156\pi\) | |||||||
\(972\) | 15.0084 | 0.481393 | ||||||||
\(973\) | 5.58647 | 0.179094 | ||||||||
\(974\) | −3.17486 | −0.101729 | ||||||||
\(975\) | 32.5922 | 1.04379 | ||||||||
\(976\) | 8.67190 | 0.277581 | ||||||||
\(977\) | −29.1378 | −0.932200 | −0.466100 | − | 0.884732i | \(-0.654341\pi\) | ||||
−0.466100 | + | 0.884732i | \(0.654341\pi\) | |||||||
\(978\) | −48.8389 | −1.56169 | ||||||||
\(979\) | 7.70483 | 0.246247 | ||||||||
\(980\) | −6.18300 | −0.197509 | ||||||||
\(981\) | −55.4335 | −1.76985 | ||||||||
\(982\) | 8.43582 | 0.269198 | ||||||||
\(983\) | 56.2213 | 1.79318 | 0.896591 | − | 0.442860i | \(-0.146036\pi\) | ||||
0.896591 | + | 0.442860i | \(0.146036\pi\) | |||||||
\(984\) | −3.31695 | −0.105741 | ||||||||
\(985\) | 6.22408 | 0.198316 | ||||||||
\(986\) | 1.55580 | 0.0495469 | ||||||||
\(987\) | −67.8875 | −2.16088 | ||||||||
\(988\) | 6.42387 | 0.204370 | ||||||||
\(989\) | 16.4889 | 0.524316 | ||||||||
\(990\) | 7.41885 | 0.235786 | ||||||||
\(991\) | −16.0486 | −0.509800 | −0.254900 | − | 0.966967i | \(-0.582043\pi\) | ||||
−0.254900 | + | 0.966967i | \(0.582043\pi\) | |||||||
\(992\) | −6.19809 | −0.196790 | ||||||||
\(993\) | −8.15204 | −0.258697 | ||||||||
\(994\) | 48.7467 | 1.54615 | ||||||||
\(995\) | −13.3044 | −0.421779 | ||||||||
\(996\) | 30.2962 | 0.959972 | ||||||||
\(997\) | 22.6280 | 0.716636 | 0.358318 | − | 0.933600i | \(-0.383350\pi\) | ||||
0.358318 | + | 0.933600i | \(0.383350\pi\) | |||||||
\(998\) | −27.6674 | −0.875797 | ||||||||
\(999\) | −8.52439 | −0.269700 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8026.2.a.d.1.11 | ✓ | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.d.1.11 | ✓ | 96 | 1.1 | even | 1 | trivial |